Both known and novel methods exist that use multiple receivers having known locations to solve for the position of unknown transmitters, which can be both stationary and in motion. One novel method geolocating moving or fixed transmitters using time difference of arrival (TDOA) and/or frequency difference of arrival (FDOA) at multiple observing receivers is disclosed in co-pending U.S. patent application Ser. No. 11/464,762, the disclosure of which is incorporated herein in its entirety. What is common among these known and novel methods is that they attempt to solve for an unknown transmitter location or path based on signals received at known locations. Disclosed herein is the use of similar principles to solve a somewhat related problem, to wit, assuming that a plurality of potential transmitter paths are known, analyzing signals received by observers at known locations to determine whether something is transmitting along one of the known paths.
Numerous conventional techniques exist to perform to perform conventional geolocation based on various physical properties of transmission signals. It is helpful to examine some of the properties of signals that may be measured as background to determine which techniques may be borrowed to solve the problems to which embodiments of the instant invention are directed. For example, multiple receivers receiving from a single transmitter can detect differences in the angle-of-arrival (AOA) or phase-of-arrival (POA) of the received signal. In the event that one or more of the receivers is moving, the receivers can also detect differences in the frequency-of-arrival (FOA), or in some instances use receiver motion to synthesize an aperture. These parameters as well as TDOA may be used to detect the transmitter's position.
It is useful to examine the properties of narrow-band signals from unknown transmitters and what information can be measured by receivers by conventional methods.
A first quantity of interest is time of arrival or TOA. It is common to consider the TOA of a narrowband signal's modulation envelope separately from the signal's carrier phase, even though these two parameters are related. In a uniform propagation medium the TOA of a received signal is given by:TOA=TOT+Range/Vg, where
TOA is the time of arrival;
TOT is the time of transmission
Range is the distance between the receiver and transmitter; and
Vg is the group velocity or velocity of the modulation envelope.
A next quantity of interest is phase of arrival or POA. The phase of arrival (POA) of the received signal is given by:POA=POT−(Fcarrier*Range/Vp)+K, where
POT is the phase of the signal at transmission in cycles (or fractions of cycles)
Fcarrier is the carrier frequency
Range is the distance between the receiver and transmitter;
Vp is the phase velocity, which is the velocity of the carrier wave; and
K is a constant representing phase biases in the system.
Unfortunately, when the task is to locate an unknown transmitter, the transmitted waveform may be unknown, and what is more, may not a simple waveform, i.e., may not include a simple sinusoidal carrier waveform of a single frequency. In such cases, the carrier waveform may be thought of as any Fourier component of the transmitted signal that is selected for measurement. Additionally, or alternatively, narrowband filtering of the measured signal may be used to isolate a single frequency component of the received signal.
Additionally, it is important to note that the group and phase velocities of a signal may not always be equal. In a dispersive medium, where the propagation speed varies with frequency, group and phase velocities may be unequal. While group velocity must always be slower than the speed of light in vacuum, phase velocity can actually exceed the speed of light. In the ionosphere, for example, phase velocity is faster than the speed of light by the same amount as group velocity is slower than the speed of light. For the purposes of this Detailed Description, however, group and phase velocities will be assumed to be equal to one another and to c, the speed of light in vacuum.
Frequency is the rate of change of phase. The phase measured at a receiver may also change if the receiver or transmitter are moving. Frequency is conventionally measured in terms of cycles per unit time or hertz. If the path length between the receiver and the transmitter is changing over time, the received carrier frequency will be Doppler shifted by an amount equal to the negative rate of change of the length of the path from the transmitter to the receiver measured in wavelengths. The Doppler shifted frequency is given by:Fd=−Vr/λ, where
Fd is the Doppler shift in frequency;
Vr is the radial velocity or the rate of change of the path length between receiver and transmitter; and
λ is the wavelength of the carrier.
Another parameter of interest in locating signals using TDOA is the group delay, which is the delay of the modulation envelope of a received signal with respect to a reference time. This quantity is given byGroup Delay=−dΦ/df, where
Φ is the phase of a frequency component of a signal; and
dΦ/df is the derivative of phase with respect to frequency.
This relationship between group delay and phase as a function of frequency is useful when measuring a signal's group delay using cross spectral analysis since the amount of the group delay misalignment is inversely proportional to the cross-spectrum's phase slope with respect to frequency.
A next quantity of interest is frequency of arrival or FOA. The frequency of an arriving signal is the frequency of the carrier of the signal minus any Doppler shift, which is given by:FOA=Fc−Vr/λ, where
Fc is the carrier frequency;
Vr is the rate of change along the path between receiver and transmitter; and
λ is the wavelength of the received signal.
In certain situations the carrier Fc may be unknown, and may drift with time due to transmitter oscillator instability.
A next quantity of interest is angle of arrival or AOA. Measuring the angle of arrival of an incoming signal can be accomplished by two or more phased antenna elements located at a known distance and orientation from one another to measure the differential phase of a signal between the elements. Alternatively, if assumptions are made about transmitter carrier stability (i.e., if it is assumed that the transmitter carrier does not experience random phase changes), moving antenna elements can be used to synthesize an antenna beam by measuring the phase front of an incoming signal with a moving element or elements.
A next quantity of interest is time difference of arrival or TDOA. As is sort forth above, the time of a signal's transmission (TOT) is generally not known, except in special cases. Accordingly, it is common to measure the TDOA at two separated receivers to eliminate the unknown TOT. This is accomplished according to the following.TOA1=TOT+Range1/Vg TOA2=TOT+Range2/Vg TDOA=TOA1−TOA2=(Range1−Range2)/Vg, where
TOA1 is the time of arrival at receiver 1
Range1 is the distance between receiver 1 and the transmitter
TOA2 is the time of arrival at receiver 2; and
Range2 is the distance between receiver 2 and the transmitter.
Measuring TDOA with two fixed receivers having known locations defines a hyperbolic surface on which the transmitter must lie, with the two receivers located at the two foci of the hyperboloid.
A next quantity of interest is frequency difference of arrival or FDOA. Generally, the frequency of the transmitter's carrier is unknown, but this unknown quantity can be eliminated by measuring FDOA between two observers, one of which is moving. If one receiver is fixed at a known location and the other is moving along a known path, measuring the FDOA determines a cone with a half-angle about the moving receiver's velocity vector. The location of a stationary transmitter must lie on the surface of this cone. The surface of the cone is determined by solving the following Doppler shift equation for the angleFDOA=−(V/λ)cos(Ψ), where
V is the magnitude of the moving receiver's velocity;
λ is the measured wavelength of the carrier at the receiver, and
Ψ is the angle of the transmitter relative to the moving receiver's velocity vector.
This simplified relationship assumes one stationary and one moving receiver. The more general case of two moving receivers results in a more complicated surface on which the transmitter must lie, but solving for this more complicated surface is still possible.
Conventionally, the physical properties and relationships set forth above were applied for determining the location of a transmitter over time. Take, for example, the unknown location of a emergency locator beacon from a downed aircraft or, more generally, an emergency position indicating radio beacon. A moving receiver, for example, a satellite, would measure a received frequency versus time. Since the unknown transmitter is assumed to be on the surface of the earth, one unknown dimension in the problem is already solved for, and accordingly, one only needs to determine two additional geometrical unknowns: latitude and longitude. Unfortunately, the transmitter's transmission frequency is generally unknown, for example, because of manufacturing tolerances. Additionally, the frequency of the transmitter may drift over time. Accordingly, transmission frequency and the extent of transmitter frequency drift must be estimated. This complicates the problem, moving the number of unknowns from 2, x and y position, to 3 to 4 unknowns.
In order to solve a set of equations, one must have at least as many independent equations reflecting measurements of known parameters as unknown variables. The conventional practice is to measure as many of the quantities discussed above as possible resulting in an over-determined data set, and then to use some numerical method to iteratively adjust potential values of the unknown parameters to minimize the residual errors between actual measurements and the modeled data. Such numerical methods of solving non-linear equations are conventionally known in the art.
Similar principles to the emergency locator beacon apply if the positions of the transmitter and receiver are reversed. For example, if one receiver is located on a vehicle at the earth's surface and the transmitter is located in orbit, for example, the Doppler equations are similar to those found in the emergency locator beacon problem. This is because the geometry is identical, which allows the same simplifying assumptions, but the propagation direction of the signal is reversed. This was the situation faced in establishing the U.S. Navy's Transit satellite navigation system for ship location. This problem was complicated by the fact that ship motion introduced additional unknown parameters, i.e., the ship's course and speed, which affected the Doppler measurements. However, ship motion could be determined locally, e.g., by reading a magnetic heading and measuring speed through the water. Additionally, ship speed was generally much slower than the speed of the satellite across the sky, which allowed for further simplifying assumptions.
In considering the methods used to solve for unknown parameters in TDOA and FDOA space it is useful to set forth the difference between resolution and estimation. It is known that measurements such as TDOA and FDOA have a fundamental resolution limit, which are approximately 1/bandwidth of the receiver for TDOA and 1/(observation time) for FDOA. There are methods, however, of estimating the actual values of measured parameters within these resolution limits. For example, if there are two receivers and a single strong target signal, cross correlation can be performed between the two receivers to estimate signal parameters more accurately than fundamental resolution limits would otherwise allow. Additionally, there are “super resolution” techniques, which are typically applied to AOA measurements, that allow for several signals to be present within the same resolution cell (that is where several signal parameters can not normally be resolved within the resolution limit) and still be individually estimated more accurately than the size of the resolution cell.
Conventional methods of TDOA/FDOA based geolocation generally require that unknown parameters be located in TDOA and/or FDOA space to solve for a transmitter's location. One way of measuring unknown parameters is to start with a representation of an ideal waveform and modify it's parameters such as TOA, FOA, etc. until the resulting modified waveform matches the observed waveform. Multiplying the observed waveform by the complex conjugate of the modified waveform forms a “matched filter”. If the observed signal is matched to the modified waveform, a larger averaged multiplication product results than if the waveform doesn't match. This process allows for an iterative convergence to the transmitted waveform based on evaluating and discarding estimates of the waveform.
An early application of such matched filtering was detecting modulated radar pulses buried in noise. Pulse compression was achieved by matching the received signal with the transmitted signal modified in delay and Doppler. Often a search was performed over delay-Doppler space with many different matched filters designed with slightly different delay and Doppler parameters. A 2-dimensional surface with axis of delay and Doppler could be generated with the height of the surface determined by the magnitude of the filters' output. Periodicities or other features of the signal modulation sometimes resulted in strong responses at other delay-Doppler values than the correct one. Because these responses resulted in ambiguous potential locations derived from the radar, the delay-Doppler response became known as the ambiguity function.
In a like manner, the cross-correlation between two receivers could produce an ambiguous result in TDOA-FDOA space. Accordingly, the result of cross-correlating waveforms from two receivers with different offsets in TDOA and FDOA became known as the cross-ambiguity function or CAF. Computation of the cross-ambiguity function generally requires electronic hardware or software, however, there is nothing in principle that dictates that a cross-ambiguity function must be computed with either analog or digital hardware. However the trend has been from analog to digital as technology evolves. Early methods of solving the ambiguity function involved “brute force” computational approaches where each delay and Doppler point in the ambiguity function is calculated by shifting the two waveforms in delay and Doppler, multiplying them, and integrating to form an estimate of the cross-correlation value at the corresponding delay and Doppler.
As an alternative to “brute force” fast Fourier transform (“FFT”) methods were developed to accelerate FDOA processing. An early observation with the “brute force” method set forth above was that one could increase integration time and simultaneously search many Doppler bins by using a FFT applied to the complex product of the correlator output. A typical situation might be searching a kilohertz range in FDOA with 1 Hz resolution produced by coherent integration of 1 second. The solution was to start with an integration time T on the order of a millisecond. An integration of 1 millisecond with no windowing results in a sin(x)/x type frequency response with nulls at +/−1 kHz.
The complex cross-correlation estimates at each lag value were input as a complex time sequence to a computer, appropriately windowed and FFTed. For example, with N=1024 and T=1 millisecond (1 kHz data rate), 1,024 frequency bins with a width of about 1 Hz and spaced about 1 Hz result.
Even if the FDOA was changing with time, it was possible to apply a “dechirp” to one of the correlator legs and then increase the integration. If N=64K in the above example, then Doppler resolution and spacing can be reduced to about 0.015 Hz while coherent integration can be increased to over a minute.
Eventually digital filters began using FFTs instead of “brute force” tapped delay lines and multipliers to implement filters. The same concepts enable cross-correlation to be performed more efficiently using FFTs.
One example of this technology was a transmultiplexer. A transmultiplexer forms a bank of adjacent narrowband filters. So, for, example, a transmultiplexer with an input data rate of 10M complex samples per second using FFTs of 8,192 points will have channels spaced 1.2 kHz apart and resolution of roughly the same.
Such channels have impulse response duration on the order of 1/Bandwidth or about a millisecond. The cross-spectrum between two such channels can be computed by multiplying and integrating (with a complex conjugate inserted) two such channel banks on a channel-by-channel basis.
In the transmultiplexer method, the problem of not knowing the signal-bandwidth and frequency in advance is largely solved. The channel bank separates signals that lack complete frequency overlap. For signals that overlap in frequency but are separated in FDOA, the signals can still end up being resolved.
The complex cross-spectrum of a particular frequency bin will have a phase that changes slowly with time if the signal component in that bin is near the geolocation corresponding to the bulk TDOA and FDOA. A slowly varying phase with time indicates a slight FDOA mismatch which, in turn, indicates that the energy is located at a slightly different location than corresponding to the bulk FDOA. The sample rate out of each filter is slow, corresponding to the Nyquist frequency of a narrowband filter. In order to accommodate signals that are slightly offset from the bulk FDOA setting, the complex cross-spectral output of each channel can be subject to an additional FFT of N samples in the same manner as described above. In this manner, long-duration coherent integration with resulting fine FDOA resolution can be performed.
Different frequency bins across the processing band that contain energy from the same transmitter will have similar FDOAs. Software then forms clusters in FDOA and associates energy from within an FDOA cluster together. In this manner, the frequency, bandwidth, and spectral shape of associated signal energy is determined. An important detail is that the FDOA of different frequency bins will be slightly different due to the fact that at a fixed range rate the FDOA magnitude of higher frequency energy will be proportionately larger than the FDOA magnitude of lower frequency energy.
Once energy from multiple frequency bins is associated with one transmitter, the phase slope vs. frequency of energy from these bins can be computed. This phase slope vs. frequency is the precise TDOA offset of that signal from the bulk TDOA setting.
A background in the basic problems involved with geolocation has been provided. It has been shown that one method for geolocation requires a solution for unknown parameters in TDOA and FDOA parameter space, and that several conventional methods exist for providing this solution. The basic problem to be solved by conventional methods is to locate the unknown position of a transmitter on the basis of measurements of received signals by one or more receivers.
Known methods exist for locating cooperative transmitters, i.e., transmitters for which information about the transmission is known in advance. Locating non-cooperative transmitters, i.e., transmitters transmitting arbitrary signals, is an important and more difficult problem. Additionally, while, measurements of FOA, TOA, TDOA, FDOA, and AOA are commonly used in various combinations to located fixed transmitters, there are few easy methods for locating moving transmitters. This is because moving transmitters introduce additional Doppler shifts that are difficult to distinguish when performing FDOA measurements using moving receivers.
A significant problem, indeed perhaps the most significant problem, in locating moving transmitters is determining their path, or their velocity over time. It has long been known that if the velocity vector of a transmitter were known, one could compensate for the motion and make a new mapping of TDOA/FDOA into geolocation. A common approach to locating a moving transmitter is to attempt to model the transmitter motion and then estimate the unknown model parameters by making more measurements than model unknowns. For example, one might assume that course and speed are constant over the observation interval. Then only 4 unknown parameters must be estimated; latitude, longitude, course, and speed. If this assumption is valid, then good results might be obtained. Otherwise, one can hope that an inconsistency in data residuals would suggest that the assumption was invalid. With many changes in course and speed, however, as might be present in a land vehicle, this approach fails.
What is needed, and what is disclosed in the detailed description below, is a method and system that allows for detection of transmissions from moving transmitters emitting arbitrary signals, where the moving transmitters can experience frequent path changes.